Answer :
Sure! Let's add the two polynomials step by step.
We are given two polynomials:
1. [tex]\( 7x^3 + 2x^2 - 5x - 7 \)[/tex]
2. [tex]\( x^3 - 5x^2 + 4x - 5 \)[/tex]
To add these polynomials, we will combine like terms. Like terms are terms that have the same variable raised to the same power.
1. Combine the [tex]\( x^3 \)[/tex] terms:
- [tex]\( 7x^3 \)[/tex] from the first polynomial
- [tex]\( x^3 \)[/tex] from the second polynomial
Adding these, [tex]\( 7x^3 + x^3 = 8x^3 \)[/tex]
2. Combine the [tex]\( x^2 \)[/tex] terms:
- [tex]\( 2x^2 \)[/tex] from the first polynomial
- [tex]\(-5x^2\)[/tex] from the second polynomial
Adding these together, [tex]\( 2x^2 - 5x^2 = -3x^2 \)[/tex]
3. Combine the [tex]\( x \)[/tex] terms:
- [tex]\(-5x\)[/tex] from the first polynomial
- [tex]\(4x\)[/tex] from the second polynomial
Adding these, [tex]\(-5x + 4x = -x\)[/tex]
4. Combine the constant terms:
- [tex]\(-7\)[/tex] from the first polynomial
- [tex]\(-5\)[/tex] from the second polynomial
Adding these, [tex]\(-7 - 5 = -12\)[/tex]
Now, put all the terms together:
The sum of the two polynomials is [tex]\[ 8x^3 - 3x^2 - x - 12 \][/tex]
That's the final simplified result!
We are given two polynomials:
1. [tex]\( 7x^3 + 2x^2 - 5x - 7 \)[/tex]
2. [tex]\( x^3 - 5x^2 + 4x - 5 \)[/tex]
To add these polynomials, we will combine like terms. Like terms are terms that have the same variable raised to the same power.
1. Combine the [tex]\( x^3 \)[/tex] terms:
- [tex]\( 7x^3 \)[/tex] from the first polynomial
- [tex]\( x^3 \)[/tex] from the second polynomial
Adding these, [tex]\( 7x^3 + x^3 = 8x^3 \)[/tex]
2. Combine the [tex]\( x^2 \)[/tex] terms:
- [tex]\( 2x^2 \)[/tex] from the first polynomial
- [tex]\(-5x^2\)[/tex] from the second polynomial
Adding these together, [tex]\( 2x^2 - 5x^2 = -3x^2 \)[/tex]
3. Combine the [tex]\( x \)[/tex] terms:
- [tex]\(-5x\)[/tex] from the first polynomial
- [tex]\(4x\)[/tex] from the second polynomial
Adding these, [tex]\(-5x + 4x = -x\)[/tex]
4. Combine the constant terms:
- [tex]\(-7\)[/tex] from the first polynomial
- [tex]\(-5\)[/tex] from the second polynomial
Adding these, [tex]\(-7 - 5 = -12\)[/tex]
Now, put all the terms together:
The sum of the two polynomials is [tex]\[ 8x^3 - 3x^2 - x - 12 \][/tex]
That's the final simplified result!